In much of our earlier work on the foundations of imprecise—or indeterminate [1]}—probabilities [2]}, [3]} we availed ourselves of binary preference orders between uncertain rewards to model a subject's decisions under uncertainty; see [4]}, [5]}, [6]}, [7]}, [8]}, [9]} for a few representative examples.
In the field, the monikers `desirability' and `sets of desirable gambles' are typically used to describe uncertainty models involving such (strict) binary preference orders [10]}, [6]}, [8]}, [13]}, [14]}.
In earlier work, Seidenfeld et al. [15]} also introduced the term `favourability' for this.
